In most estimation and detection problems, one or more parameters describing an underlying physical process must be estimated from measured or empirical data. For example, in remote sensing applications, the goal of estimation is to obtain some information about the underlying structure of subsurface anomalies (e.g., land mines, tumors, etc.) by analyzing data obtained from a sensor. Most estimation problems assume that the data are random and have a probability distribution dependent on the parameters of interest. The data are also often assumed to include noise.
In most detection problems, the goal of detection is to discern, under conditions of uncertainty, whether or not a signal of interest exists in data by making decisions. In such problems a threshold test is often employed to partition data believed to contain the signal of interest from data believed to contain only noise.
Detection problems can be described as a hypothesis test in which two types of misclassification errors are possible: false positive decision (i.e., false alarm) and false negative decision. A false positive decision can be made when a null hypothesis is incorrectly rejected despite being true. A false negative decision occurs when a null hypothesis is not rejected despite its being false. This may be generalized to hypothesis testing (i.e., classification problems) in which misclassification errors are also possible and are characterized by a confusion matrix. In the generalization to hypothesis testing, thresholds are generalized to decision boundaries and similar tradeoffs extend to the associated misclassification rates.
Most detection problems require that a threshold be determined prior to making a decision. Based on the determined threshold, any data value greater than the threshold is considered to include the signal of interest and any data value falling below the threshold level is considered to be noise and/or clutter. If this threshold is lowered, then the detection rate will increase and the number of false alarms will also increase. Lower false alarm rates may be achieved by increasing the threshold levels but this will result in a decreased detection rate.
In the simplest detection problems, the noise and/or clutter statistics are taken as a priori information so that the test threshold may be computed in advance to achieve a desired false alarm rate. However, since complete knowledge of noise statistics is not typically possible (as this would require clairvoyance), noise or clutter statistics must be modeled and model parameters must be estimated [7]. In such cases, Constant False Alarm Rate (CFAR) detection techniques may be used to determine threshold levels that ensure a prescribed false alarm rate. For example, some CFAR techniques may adaptively change the threshold levels in accordance with the changing statistics of the background noise or clutter in which the signals are to be detected [8]. However, most CFAR techniques still make some assumption about the noise model or the parameters thereof to ensure the prescribed performance level is achieved.
Distribution-Free Tolerance Intervals (DFTI) [3]-[5] may be used to formulate tests that are not reliant on assumptions of noise and/or clutter model or parameters thereof [1], [2]. For example, detectors employing DFTI may have constant false alarm rates (CFAR) at a prescribed level, a, regardless of the statistics of their background noise. Such detectors are, therefore, robust to the model and parameter uncertainty to which commonly used detectors are sensitive [6].